As semiconductor devices are being miniaturized further, use of extreme ultraviolet (EUV) light in photolithography is under consideration. In EUV exposure, a reflecting optical system and a reflective photomask are used.
The surface of a mirror of the reflecting optical system cannot be made completely flat, permitting a roughness in the mirror surface. Therefore, exposure light reflects diffusely at the mirror surface. The diffusely reflected exposure light is also applied to a region which should normally be unexposed on the semiconductor wafer surface (or photoresist surface). The exposure light diffusely reflected and applied to the wafer surface is called flare.
When flare has occurred, the contrast of exposure light decreases and a desired resist pattern cannot be formed. The amount of flare depends on a surrounding pattern density. Therefore, the following problem arises: even if patterns are the same in design size, patterns differing in size according to a variation in the surrounding pattern density are formed on a semiconductor wafer.
To prevent the problem, it is important to predict a flare distribution in advance and perform correction. A flare distribution is predicted as follows.
First, a pattern layout (or design layout) is partitioned into a plurality of regions in mesh form. A pattern density is calculated for each of the partitioned regions to make a density map. Then, the convolution of a point spread function (PSF) and the density map is calculated to produce a flare map (or a flare distribution).
However, the flare map made as described above has only one flare value for each partitioned region (or each mesh). Therefore, when flare has changed significantly in a mesh, a flare value cannot be determined with high accuracy. To determine a high-accuracy flare distribution, it is necessary to make a partition size (or a mesh size) smaller. When the partition size is made smaller, the computation time increases significantly. For example, the length of one side of a mesh is halved, the calculation amount to determine flare values for all the meshes represents a 16-fold increase.
As described above, the conventional art has the problem of requiring an enormous computation time to predict flare with high accuracy.